[Paper Review] Inverse dynamical population synthesis: Constraining the initial conditions of young stellar clusters by studying their binary populations

Michael Marks, Pavel Kroupa|arXiv (Cornell University)|May 7, 2012

Astrophysics and Star Formation Studies104 references110 citations

TL;DR

This paper proposes that dynamical evolution alone—without varying initial binary properties—can explain the observed multiplicity fractions and orbital distributions in diverse young stellar clusters. By applying inverse dynamical population synthesis to N-body models, it shows that varying initial cluster densities (from 1 to 2×10⁴ stars pc⁻³) reproduce observed binary populations in Taurus, Orion, IC 348, and others, revealing a weak stellar mass–half-mass radius correlation: r_h ∝ M_ecl^0.13±0.04.

ABSTRACT

Binary populations in young star clusters show multiplicity fractions both lower and up to twice as high as those observed in the Galactic field. We follow the evolution of a population of binary stars in dense and loose star clusters starting with an invariant initial binary population and a formal multiplicity fraction of unity, and demonstrate that these models can explain the observed binary properties in Taurus, Rho-Ophiuchus, Chamaeleon, Orion, IC 348, Upper Scorpius A, Praesepe, and the Pleiades. The model needs to consider solely different birth densities for these regions. The evolved theoretical orbital-parameter distributions are highly probable parent distributions for the observed ones. We constrain the birth conditions (stellar mass, M_ecl, and half-mass radius, r_h) for the derived progenitors of the star clusters and the overall present-day binary fractions allowed by the present model. The results compare very well with properties of molecular cloud clumps on the verge of star formation. Combining these with previously and independently obtained constraints on the birth densities of globular clusters, we identify a weak stellar mass -- half-mass radius correlation for cluster-forming cloud clumps, r_h / pc ~ (M_ecl / M_sun)^(0.13+-0.04). The ability of the model to reproduce the binary properties in all the investigated young objects, covering present-day densities from 1-10 stars pc^-3 (Taurus) to 2x10^4 stars pc^-3 (Orion), suggests that environment-dependent dynamical evolution plays an important role in shaping the present-day properties of binary populations in star clusters, and that the initial binary properties may not vary dramatically between different environments.

Motivation & Objective

• To determine whether environment-dependent dynamical evolution can explain observed binary population properties in young star clusters without assuming environment-dependent initial binary formation.
• To constrain the initial conditions (stellar mass M_ecl and half-mass radius r_h) of observed young clusters using inverse modeling of binary evolution.
• To test whether a universal initial binary population can reproduce observed multiplicity fractions across clusters with vastly different present-day densities.
• To derive a scaling relation between cluster mass and size at birth from dynamical constraints, linking cluster formation to molecular cloud clump properties.

Proposed method

• The study uses inverse dynamical population synthesis to infer initial cluster conditions from observed binary properties in eight young clusters.
• N-body simulations model the evolution of a binary-rich population starting from a universal initial binary distribution with unity multiplicity fraction.
• The method inverts observed orbital parameter distributions to infer the initial cluster density, mass, and half-mass radius that best reproduce the data.
• Initial conditions are constrained by matching theoretical evolved binary distributions to observed distributions in Taurus, ρ Ophiuchus, Chamaeleon, Orion, IC 348, Upper Scorpius A, Praesepe, and the Pleiades.
• The analysis incorporates constraints from previous studies on globular cluster birth densities to extend the relation to a broader range of cluster masses.
• A power-law scaling relation r_h ∝ M_ecl^0.13±0.04 is derived from the combined data, linking cluster size to mass at birth.

Experimental results

Research questions

• RQ1 Can dynamical evolution alone explain the observed range of binary fractions in young star clusters with varying present-day densities?
• RQ2 What are the initial cluster conditions (M_ecl, r_h) required to reproduce the observed binary populations in Taurus, Orion, IC 348, and other clusters?
• RQ3 Is there a universal initial binary population that can account for the observed multiplicity properties across diverse environments?
• RQ4 Does the observed variation in binary populations reflect initial formation differences or post-formation dynamical evolution?
• RQ5 What is the intrinsic relationship between cluster mass and half-mass radius at birth, as inferred from dynamical modeling?

Key findings

• The model successfully reproduces observed binary multiplicity fractions and orbital distributions in all eight investigated young clusters using only variations in initial cluster density.
• Taurus, with low present-day density (~1–10 stars pc⁻³), hosts a largely unevolved binary population consistent with a low initial density of ~10 stars pc⁻³.
• Orion, with high present-day density (~2×10⁴ stars pc⁻³), requires a high initial density (~10⁴ stars pc⁻³) to match observed binary properties.
• IC 348 and the Pleiades, along with Praesepe, ρ Ophiuchus, and Chamaeleon, share similar inferred initial densities, indicating comparable dynamical evolution histories.
• The study reveals a weak but significant correlation between initial cluster mass and half-mass radius: r_h / pc ∝ (M_ecl / M☉)^0.13±0.04, consistent with molecular cloud clump observations.
• The results support the hypothesis of a universal initial binary population, with observed variations in binary properties arising primarily from dynamical evolution rather than initial formation differences.